Recently I wrote a review of Between the Lines, a helpful handbook on bio-medical statistics authored by an acquaintance and colleague, Dr. Marya Zilberberg. In that post, I mentioned my concern about some of the assumptions and statements on mammography. One thing I liked the book, abstractly, is the author’s efforts to streamline the discussion so that the reader can follow the concepts. But simplification and rounding numbers, “for ease of presentation” (p. 29) can mess up facts, significantly in ways that some primary care doctors and journalists might not appreciate. And so I offer what I hope is a clarification, or at least an extension of my colleague’s work, for purposes of helping women understand the potential benefits and risks of mammography.

In the section on mammography (pp. 28-31), the author rounds down the incidence of breast cancer in women between the ages of 40 and 50 years, from “1 in 70” (1.43%) to “1 in 100” (1%). As any marketing professional might remind us, this small change represents a 30% drop (0.43/1.43) in the rate of breast cancer in women of that age group. This difference – of 30%, or 43%, depending on how you look at it – will factor into any calculation of the false positive (FP) rate and the positive predictive value (PPV) of the test.

For women ages 40-49

Have breast cancer

Don’t have breast cancer

If estimate 1 in 100, 1.0 %

100

9,900

If estimate 1 in 70, 1.43 %

143

9,857

Keep in mind that these same, proportional difference would apply to any BC screening considerations – in terms of the number of women affected, the potential benefits and costs, for the 22,996,493 women between the ages of 40 and 49 counted in the 2010 U.S. Census,

My colleague estimates, fairly for this younger age group of women (who are relatively disposed to fast-growing tumors), that the screening technology (mammography) only picks up 80% of cases; 20% go undetected. In other words – the test is 80% sensitive; the false negative, FN, rate is 20%. In this same section, she considers that the FP rate as 10%. Let’s accept this (unacceptably high) FP rate for now, for the sake of discussion.

As considered in Between the Lines:

If FP rate is 10%, prevalence 1 in 100

Really have BC

Don’t have BC

Total

Mammography +

80

990

1,070

Mammography –

20

8,910

8,930

Total

100

9,900

10,000

But the above numbers aren’t valid, because the disease affects over 1 in 70 women in this age bracket. Here’s the same table with a prevalence of 1 in 70 women with BC:

If FP rate is 10%, prevalence 1 in 70

Really have BC

Don’t have BC

Total

Mammography +

114

986

1,100

Mammography –

29

8,871

8,900

Total

143

9,857

10,000

In this closer approximation to reality, the number of true positives is 114, and false positives 986, among 1,100 abnormal screening results. Now, the PPV of an abnormal mammogram is 114/ (114+986) = 10.4%. So the main statistical point – apart from the particulars of this discussion – is that a seemingly slight rounding down can have a big impact on a test’s calculated and perceived value. By adjusting the BC rate to its prevalence of approximately 1 in 70 women between 40 and 49 years, we’ve raised the PPV from 7.5% to 10.4%.

Here I must admit that I, too, have rounded, although I did so conservatively very slightly. I adopted a 1 in 70 approximation (1.43%) instead of 1 in 69 (1.45%), as indicated on the NCI website. If we repeat the table and figures using a 1 in 69 or 1.45% prevalence rate and 6% FPS, the PPV rises a tad, to 10.5%.

Now, we might insert a different perspective: What if the false positive rate were 6%, as has been observed among sub-specialist radiologists who work mainly in breast cancer screening?

If FP rate is 6%, prevalence 1 in 70

Really have BC

Don’t have BC

Total

Mammography +

114

591

705

Mammography –

29

9266

9,295

Total

143

9,857

10,000

As you can see, if we use a FP rate of 6% in our calculations, the total number of FPs drops to 591 among 10,000 women screened. In this better-case scenario, the PPV of the test would = 114/ (114+591) =16%. Still, that’s not great – and I’d argue that public health officials, insurers and patients should be pushing for FP rates closer to 2 or 3% – but that’s irrelevant to my colleague’s point and her generally instructive work.

My second concern has to do with language, and making the consequences of false positives seem worse than they really are. On page 29, the author writes: “ So, going back to the 10,000 women being screened, of 9,900 who do NOT have cancer… 10%, or 990 individuals will still be diagnosed as having cancer.” The fact is, the overwhelming majority of women with positive mammograms won’t receive a cancer diagnosis. Rather, they’ll be told they have “an abnormal result, or a finding that suggests the possibility of cancer and needs further evaluation,” or something along those lines. It would be unusual in practice to jump from a positive mammogram straight to a breast cancer diagnosis. There are steps between, and every patient and journalist should be aware of those.

—
Finally, if I were to write what I really think, apart from and beyond Between the Lines – I’d suggest the FP rate should be no higher than 2 or 3% in 2012. This is entirely feasible using extant technology, if we were to change just two aspects of mammography practice in the U.S. First, require that all mammograms be performed by breast radiologists who get extra training and focus in their daily work almost exclusively on breast imaging. Second, make sonograms – which, together with mammograms, enhance the specificity of BC screening in women with dense breasts– universally available to supplement the radiologists’ evaluations of abnormal mammograms and dense breasts in younger women.

By implementing these two changes, essentially supporting the practice of sub-specialists in breast radiology, we could significantly lower the FP rate in breast cancer screening. The “costs” of those remaining FPs could be minimized by judicious use of sonograms, needle biopsies and other measures to reduce unnecessary surgery and over-treatment. Over the long haul, we need to educate doctors not to over-treat early stage disease, but that goes far beyond this post and any one woman’s analysis of mammography’s effectiveness.

One Comment

Elaine, thank you for this excellent post! You really did a great job pointing out how important the pre-test probability is to interpreting any test. As for increases in the PPV that you illustrate, while they are certainly there, each woman should be given tools to decide for herself whether they are substantial enough to influence her decision.